please answer all parts clearly with all work, thanks **Educational Module: Computational Complexity Analysis****Objective:**Determine the largest size \( n \) of a problem that can be solved in a given time \( t \) for various functions \( f(n) \), under the assumption that solving the problem takes \( f(n) \) microseconds.**Time Conversion Key:**- \( 1 \) second \( = 10^6 \) microseconds- \( 1 \) minute \( = 60 \times 1 \) second- \( 1 \) hour \( = 60 \times 1 \) minute- \( 1 \) day \( = 24 \times 1 \) hour- \( 1 \) month \( = 28 \times 1 \) day- \( 1 \) year \( = 12 \times 1 \) month- \( 1 \) century \( = 100 \times 1 \) year**Table for Problem Size Analysis:**| Function \( f(n) \) | 1 Minute | 1 Day | 1 Year ||---------------------|---------|-------|--------|| \( \log n \) | | | || \( \sqrt{n} \) | | | || \( n\log n \) | | | || \( n^2 \) | | | || \( n^3 \) | | | || \( 2^n \) | | | || \( n! \) | | | |**Instructions:**For each function \( f(n) \), calculate the maximum \( n \) that can be solved within the given time constraints (1 minute, 1 day, 1 year) based on the conversions provided. This requires an understanding of the growth rates of each function relative to the available computational time.**Graph/Diagram Explanation:**The table is designed to help visualize how different computational complexities (such as logarithmic, linear, polynomial, exponential, and factorial) scale with time. Each cell will ultimately contain the maximum \( n \) values corresponding to solving a problem of size \( n \) within 1 minute, 1 day, or 1 year for the given time complexities.

1s=10^6 μs 1m = 60 x 1s log n Vn nlogn n² 2. For each function f(n) and time t in the following table, determine the largest size n of a problem that can be solved in time t, assuming that the algorithm to solve the problem takes f(n) microseconds. n³ 2n n! 1hr = 60 x 1m 1 day = 24 x 1hr 1 minute 1 month = 28 x 1 day 1 day 1 year = 12 x 1 month 1 year 1 century = 100 x 1 year

1s=10^6 μs 1m = 60 x 1s log n Vn nlogn n² 2. For each function f(n) and time t in the following table, determine the largest size n of a problem that can be solved in time t, assuming that the algorithm to solve the problem takes f(n) microseconds. n³ 2n n! 1hr = 60 x 1m 1 day = 24 x 1hr 1 minute 1 month = 28 x 1 day 1 day 1 year = 12 x 1 month 1 year 1 century = 100 x 1 year

Computer Networking: A Top-Down Approach (7th Edition)

7th Edition

ISBN:9780133594140

Author:James Kurose, Keith Ross

Publisher:James Kurose, Keith Ross

Chapter1: Computer Networks And The Internet

Section: Chapter Questions

Problem R1RQ: What is the difference between a host and an end system? List several different types of end...

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